March 10th, 2017, 01:02 AM  #1 
Member Joined: Mar 2016 From: Sweden Posts: 32 Thanks: 4  Stokes theorem
I am trying to figure out when and how to use Stokes theorem. I was looking at this video: and I am really confused about how he uses the theorem. About 4.30 he writes down the integral using Stokes. So if I am having a cylinder and some line integral around it. Then it doesn't matter how this line integral looks like? Seems like he is having some arbitrary line integral around that surface.. Thx! 
March 10th, 2017, 04:50 AM  #2 
Member Joined: Dec 2016 From:  Posts: 54 Thanks: 10 
Stokes theorem works in the following way: Imagine you have a vector field $\vec{A}$, and you want to calculate the integral along a path $\gamma$ (in your case, this can be the integral along a line surrounding the cylinder). Then the following holds: \begin{eqnarray} \int_{\gamma}d\vec{s}.\vec{A}=\int_{S}d\vec{S}. \vec{\nabla}\times \vec{A} \end{eqnarray} where the integral on the right hand side is over the surface $S$, and $dS$ is the differential normal surface vector. This equality holds regardless of the geometry of the problem under consideration, so it is completely general. Hope it helps 

Tags 
stokes, theorem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Stokes's Theorem and Green's Theorem  djcan80  Calculus  2  August 24th, 2016 07:28 PM 
Stokes theorem verification.  ZardoZ  Applied Math  2  June 21st, 2011 05:31 AM 
proof by using greens theorem or stokes theorem  george gill  Calculus  5  May 14th, 2011 02:13 PM 
On an alternative Stokes' theorem  Curupira  Calculus  0  October 14th, 2010 03:32 PM 
How to solve this by using Stokes theorem please?  ggyyree  Calculus  1  April 23rd, 2009 05:39 AM 